Problem: Simplify the following expression and state the condition under which the simplification is valid. You can assume that $n \neq 0$. $p = \dfrac{10(2n - 9)}{-7} \div \dfrac{3n(2n - 9)}{-3} $
Explanation: Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{10(2n - 9)}{-7} \times \dfrac{-3}{3n(2n - 9)} $ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ 10(2n - 9) \times -3 } { -7 \times 3n(2n - 9) } $ $ p = \dfrac{-30(2n - 9)}{-21n(2n - 9)} $ We can cancel the $2n - 9$ so long as $2n - 9 \neq 0$ Therefore $n \neq \dfrac{9}{2}$ $p = \dfrac{-30 \cancel{(2n - 9})}{-21n \cancel{(2n - 9)}} = -\dfrac{30}{-21n} = \dfrac{10}{7n} $